Subjects geometry

Polygon Perimeter 2746C3

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1. **State the problem:** Calculate the perimeter of the given symmetric arrow/hexagon-like polygon with specified side lengths. 2. **Identify the sides:** The polygon has vertical sides of length 6 m, short horizontal shoulders of length 2 m, and other edges that appear symmetric. 3. **Use the perimeter formula:** The perimeter $P$ of a polygon is the sum of the lengths of all its sides. 4. **Count the sides and their lengths:** - Two vertical sides: each 6 m - Two short horizontal shoulders: each 2 m - Two slanted edges (top-left and top-right) with single tick marks, equal in length - Two slanted edges (bottom-left and bottom-right) with single tick marks, equal in length - Two middle horizontal shoulder segments with double tick marks, equal in length 5. **Calculate the lengths of the slanted edges and middle horizontal segments:** Since the shape is symmetric and the problem gives only 2 m and 6 m explicitly, assume the slanted edges and middle horizontal segments are equal to the given 2 m and 6 m segments respectively. 6. **Sum all sides:** $$P = 2 \times 6 + 2 \times 2 + 2 \times 2 + 2 \times 2 + 2 \times 6 = 12 + 4 + 4 + 4 + 12 = 36$$ 7. **Final answer:** The perimeter of the polygon is $36$ meters.